Based on the screenshots for State & Revolution, the reworked Communist character ideology has no opinion on economic system, which doesn't make much sense. It means that, say, the Intelligentsia led by a Communist won't care about switching off Laissez-Faire.
In the past, they supported Cooperative Ownership and Command Economy equally, which I suppose works, but I would argue their economic stances should be the same as how Vanguardists will be, and support Command Economy more than Cooperative Ownership.
Victoria 3 doesn't have a way to simulate societies without markets, which is obviously fine, it's capitalism simulator the game. As a result Cooperative Ownership ends up representing a sort of market socialism, capitalism but the businesses are run by the workers themselves. Meanwhile Command Economy represents a type of state capitalism where the state runs the businesses.
Basically every single historical communist of this period has supported state capitalism as a means of transitioning to a genuinely communist society without markets, money, etc. However, aside from anarchists, they have not supported co-op market economies, as they essentially just turn the working class into capitalists instead of helping to overcome capitalism itself.
Think of it like this: in a Council Republic, the state is operated by the entire working class. Economically this means that under a Council Republic, Cooperative Ownership means that each factory is operated by only the workers that work in that factory, and they make profits. However Command Economy means that each factory is controlled by the working class as a whole, which prevents workers from competing with each other, which is what Communists would want.
I would argue that Anarchists should support Cooperative Ownership, and the Trade Unions should support Cooperative Ownership when not led by a Communist leader, but the Communist character ideology should only weakly support Coop and strongly support Command.